

A075869


Numbers k such that 5*k^2  9 is a square.


0



3, 51, 915, 16419, 294627, 5286867, 94868979, 1702354755, 30547516611, 548152944243, 9836205479763, 176503545691491, 3167227616967075, 56833593559715859, 1019837456457918387, 18300240622682815107
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OFFSET

1,1


COMMENTS

Lim. n> Inf. a(n)/a(n1) = phi^6 = 9 + 4*sqrt(5).


REFERENCES

A. H. Beiler, "The Pellian", ch. 22 in Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. Dover, New York, New York, pp. 248268, 1966.
L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine Analysis. AMS Chelsea Publishing, Providence, Rhode Island, 1999, pp. 341400.
Peter G. L. Dirichlet, Lectures on Number Theory (History of Mathematics Source Series, V. 16); American Mathematical Society, Providence, Rhode Island, 1999, pp. 139147.


LINKS

J. J. O'Connor and E. F. Robertson, Pell's Equation [From the Internet Archive Wayback machine]


FORMULA

a(n) = 3*sqrt(5)/10*((2+sqrt(5))^(2*n1)(2sqrt(5))^(2*n1)) = 18*a(n1)  a(n2).


MATHEMATICA

LinearRecurrence[{18, 1}, {3, 51}, 20] (* Harvey P. Dale, Dec 27 2018 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



